The quantum Ising chain for beginners

given by Giuseppe Santoro

Term: 0

Start: 11-01-2021 End: 26-02-2021 Room: 131

Credits: 3

Schedule: TBA

Program

I will present various techniques to work with quantum Ising chains. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we will review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. A few problems illustrating important aspects of the physics of this model will provide simple applications of the techniques.

More in detail, the course will consist of:

  • A crach course in scientific programming with python and with jupyter notebooks
  • The Jordan-Wigner transformation applied to one-dimensional spin-1/2 models
  • Free-fermion models (Ising/XY)
  • Translationally invariant and disordered Nambu formalism
  • Time-dependent Bogoljubov-de Gennes equations and calculation of dynamical quantities
  • Calculating thermal averages
  • Calculating correlation functions involving Jordan-Wigner strings
  • Calculating the entanglement entropy 

The course will be strongly ``hands-on based'': collaborating in small groups, we should eventually construct a python library to calculate many properties of Ising spin chains.

Online resources

Filename Size Date Modified
QuantumIsingChain_2009.09208.pdf 3.17 MB 2020-09-24 09:31:35